Physics

Thermal Properties and Thermodynamics

380 Questions

Thermal properties and thermodynamics questions evaluate concepts of heat transfer, thermal efficiency, and temperature variations. Problems involve calculating heat content, conductivity, and the performance of heat engines. This subject is regularly tested in physics sections across multiple competitive platforms.

Heat transfer calculationsThermal efficiencyBlack body radiationTemperature variationsRefrigeration performance

Thermal Properties and Thermodynamics Questions

Multiple choice physics temperature and heat modes of heat transfer - conduction conduction heat and modes of heat transfer

Three rods of identical cross-sectional area and made from the same metal from the sides of an isosceles triangles ABC, right-angled at B. The point A and B are maintained at temperatures T and $(\sqrt{2})$T respectively. In the steady state, the temperature of the point C is $T _C$. Assuming that only heat conduction takes place, $T _C/T$ is?

  1. $\dfrac{1}{2\left(\sqrt{2}-1\right)}$
  2. $\dfrac{3}{\sqrt{2}+1}$
  3. $\dfrac{1}{\sqrt{3}\left(\sqrt{2}-1\right)}$
  4. $\dfrac{1}{\sqrt{2}+1}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the steady-state heat flow condition (sum of heat currents at junction C is zero), the heat currents from A to C and B to C must balance. Given the geometry and thermal resistance, the calculation leads to the ratio 3/(sqrt(2)+1).

Multiple choice physics temperature and heat modes of heat transfer - conduction conduction heat and modes of heat transfer

If $K$ denotes coefficient of thermal conductivity, $d$ the density and $C$ the specific heat, the unit of $X$, where $X = K/dc$, will be

  1. $cm\space sec$
  2. $cm^2\space sec^{-2}$
  3. $cm \space sec^{2}$
  4. $cm^2 \space sec^{-1}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The Units of the respective quantities in SI are:

  • $[K] = J(mKs)^{-1}$
  • $[\rho] = kg(m)^{-3}$
  • $[c] = J(kgK)^{-1}$
$[X] = \dfrac{[K]}{[\rho] [c]} = \dfrac{J(mKs)^{-1}}{(kg(m)^{-3})(J(kgK)^{-1})}$
$[X] = m^{2}s^{-1}$ or in CGS $cm^{2}s^{-1}$

Multiple choice physics temperature and heat modes of heat transfer - conduction conduction heat and modes of heat transfer

A body of length 1 m have an area of cross-section as 0.75 $m^{2}$. If rate of heat conduction of the body is 6000 J/s and coefficient of thermal conductivity is 200 $Jm^{-1}$ $K^{-1}$, then the temperature difference between the two ends of the body is

  1. $30^{\circ}C$
  2. $20^{\circ}C$
  3. $40^{\circ}C$
  4. $80^{\circ}C$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using the formula Q/t = kA(dT/dx), where Q/t = 6000, k = 200, A = 0.75, and dx = 1. Rearranging gives dT = (Q/t * dx) / (kA) = (6000 * 1) / (200 * 0.75) = 6000 / 150 = 40 degrees C.

Multiple choice physics temperature and heat modes of heat transfer - conduction conduction heat and modes of heat transfer

Equal temperature difference exists between the ends of two metallic rods $1 $ and $2$ of length. Their thermal conductivities are $K _1$ and $K _2$ and cross sectional areas represents $A _1$ and $A _2$. The condition for equal rate of heat transfer is:

  1. $K _1A _2=K _2A _1$
  2. $K _1A _1=K _2A _2$
  3. $K _1A _1^2=K _2A _2^2$
  4. $K _1^2A _2=K _2^2A _1$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Equal temperature difference exists between the two metallic rods 1 and 2.
The heat transfer$=\dfrac{KA \Delta T}{l}$
For equal rate of heat transfer,
$\dfrac{K _1 A _1 \Delta T}{l}=\dfrac{K _2A _2 \Delta T}{l}$
$K _1A _1=K _2A _2$
The correct option is B.
Multiple choice physics temperature and heat modes of heat transfer - conduction conduction heat and modes of heat transfer

Same quantity of ice is filled in each of the two metal containers P and Q having the same size, shape and wall thickness but made of different materials. The containers are kept in identical surroundings. The ice in P melts completely in time $t _1$ whereas that in Q takes a time $t _2$. The ratio of thermal conductivities of the materials of P and Q is

  1. $t _2 : t _1$
  2. $t _1 : t _2$
  3. $t _1^2 : t _2^2$
  4. $t _2^2 : t _1^2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The power transported per unit area is given as

$\dfrac{\Delta Q}{A\Delta t}=-\kappa\dfrac{\Delta T}{\Delta x}$
Thus $\Delta Q=-\kappa \Delta tA\dfrac{\Delta T}{\Delta x}$
Same amount of heat was needed to melt ice in both P and Q. Hence 
$\kappa _{P}t _1=\kappa _Qt _2$
$\implies \dfrac{\kappa _P}{\kappa _Q}=\dfrac{t _2}{t _1}$

Multiple choice physics temperature and heat modes of heat transfer - conduction conduction heat and modes of heat transfer

Two plates of same thickness form a composite plate. The temperature on one side of the plate is $0^0 C$. If the ratio of thermal conductivities is 3 : 1 and the plate with higher thermal conductivity has one of its faces at $0^0 C$, then the temperature of the interface is 

  1. $45^0 C$
  2. $40^0 C$
  3. $20^0 C$
  4. $15^0 C$
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice physics temperature and heat modes of heat transfer - conduction conduction heat and modes of heat transfer

A body P is connected to a large body Q through a conducting rod of length. I crossectional  area. A and thermal conductivity K. This assembly is placed in an an atmosplere of temperature ${ T } _{ A }$ and body Q is also maintained at temperature ${ T } _{ A }$. Let beat capacity of body P is C and it is unitally at temperature ${ T } _{ 1 }$. If in time t second temperature of body P falls to ${ T } _{ 2 }$. Then chose the correct option .

  1. $log\left[ \dfrac { { T } _{ 2 }-{ T } _{ A } }{ { T } _{ 1 }-{ T } _{ A } } \right] =\left[ { K } _{ 1 }\dfrac { KA }{ LC } \right] t$
  2. $log\left[ \dfrac { { T } _{ 2 }-{ T } _{ A } }{ { T } _{ 12 }-{ T } _{ A } } \right] =\left[ { K } _{ 1 }\dfrac { KA }{ LC } \right] t$
  3. $log\left[ \dfrac { { T } _{ 1 }-{ T } _{ A } }{ { T } _{ 2 }-{ T } _{ A } } \right] =\left[ { K } _{ 1 }\dfrac { KA }{ LC } .t \right]$
  4. $log\left[ \dfrac { { T } _{ 1 }-{ T } _{ A } }{ { T } _{ 2 }-{ T } _{ A } } \right] =\left[ { K } _{ 1 }\dfrac { KA }{ LC } \right] t$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The cooling of body P follows Newton's Law of Cooling, where the rate of heat loss dQ/dt = -C(dT/dt) = (kA/L)(T - Ta). Integrating this leads to the natural log form ln((T1 - Ta)/(T2 - Ta)) = (kA/LC)t.

Multiple choice physics temperature and heat modes of heat transfer - conduction conduction heat and modes of heat transfer

A wall has two layers A and B, each made of different material. Both the layers have the same thickness. The thermal conductivity of the material of A is twice that of B. Under thermal equilibrium, the temperature difference across the wall is $36^o$C. The temperature difference across the layer A is?

  1. $6^o$C
  2. $12^o$C
  3. $18^o$C
  4. $24^o$C
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice physics temperature and heat modes of heat transfer - conduction conduction heat and modes of heat transfer

a wall has two layers $A$ and $B,$ each made of  a different material.Both the layers have the same thickness.The thermal conductivity of the material of $A$ is twice that of $B.$ Under thermal equilibrium, the temperature difference across the wall is ${36^ \circ }C$ The temperature difference across the layer $A$ is  

  1. ${6^ \circ }C$
  2. ${12^ \circ }C$
  3. ${18^ \circ }C$
  4. ${24^ \circ }C$
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice physics temperature and heat modes of heat transfer - conduction conduction heat and modes of heat transfer

An aluminium meter rod of area of cross section $4cm^2$ with K=0.5 cal $g^{-1}$ $^oC^{-1}$ is observed that at steady state 360 cal of heat flows per minute.
The temperature gradient along the rod is

  1. $3^oC/cm$
  2. $6^oC/cm$
  3. $12^oC/cm$
  4. $20^oC/cm$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Heat flow H = kA(dT/dx). Given H = 360 cal/min = 6 cal/sec, k = 0.5, A = 4. 6 = 0.5 * 4 * (dT/dx). 6 = 2 * (dT/dx), so dT/dx = 3 C/cm.

Multiple choice physics temperature and heat modes of heat transfer - conduction conduction heat and modes of heat transfer

Ratio of radius of curvature of cylindrical emitters of same type is $1:4$ and their temp. are in ration $2:1$. Then ration of amount of heat emitted by them is-(For Cylinder length = radius);-

  1. 2:1

  2. 1:1

  3. 4:1

  4. 1:4
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Power radiated P = sigma * A * T^4. For a cylinder, A = 2*pi*r*L + 2*pi*r^2. If L=r, A = 4*pi*r^2. P is proportional to r^2 * T^4. Ratio P1/P2 = (r1/r2)^2 * (T1/T2)^4 = (1/4)^2 * (2/1)^4 = (1/16) * 16 = 1:1.

Multiple choice physics temperature and heat modes of heat transfer - conduction conduction heat and modes of heat transfer

If the coefficient of conductivity of aluminium is $0.5cal/cm-sec-^oC,$ then in order to conduct $10cal/sec-cm^2$ in the steady state, the temperature gradient in aluminium must be

  1. $5^oC/cm$
  2. $10^oC/cm$
  3. $20^oC/cm$
  4. $10.5^oC/cm$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Heat flux H/A = k * (dT/dx). Given H/A = 10, k = 0.5. 10 = 0.5 * (dT/dx), so dT/dx = 20 C/cm.

Multiple choice physics temperature and heat modes of heat transfer - conduction conduction heat and modes of heat transfer

a rod of length 1 m having cross-sectional area 0.75 $m^{2}$ conduts heat at 6000 $Js^{-1}$. Then the temperature difference across the rod is, if k=200 $Wm^{-1}$ $K^{-1}$

  1. $20^{\circ}C$
  2. $40^{\circ}C$
  3. $80^{\circ}C$
  4. $1000^{\circ}C$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using H = kA(dT/L), 6000 = 200 * 0.75 * (dT/1). 6000 = 150 * dT, so dT = 40 C.

Multiple choice physics temperature and heat modes of heat transfer - conduction conduction heat and modes of heat transfer

A sphere, a cube and a thin circular plate all made of same substance and all have same mass. These are heated to $200^{o}C$ and then placed in a room. Then the:-

  1. Temperature of sphere drops to room temperature at last.

  2. Temperature of cube drops to room temperature at last.

  3. Temperature of thin circular plate drops to room temperature at last.

  4. Temperature of all the three drops to room temperature at the same time
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Rate of cooling dT/dt = (sigma * A * e * (T^4 - Ta^4)) / (m * c). For same mass and material, the body with the smallest surface area A cools the slowest. A sphere has the smallest surface area for a given volume/mass, so it takes the longest to cool.