Thermodynamics in Physics Questions and Answers

Answer: C

The statement that is not true is that conduction does not take place in gases.

Conduction transfers heat through collisions between particles, and it occurs in solids, liquids and gases. In gases the particles are far apart, so conduction is very slow (gases are poor conductors) and convection usually dominates, but it still occurs.

The other statements are true: conduction is faster in solids than in liquids, it requires contact between the objects, and different materials conduct heat differently (metals well, wood and plastic poorly).

Answer: B

The efficiency does not depend on the nature of the working substance.

Carnot efficiency is \(\eta = 1 - \frac{T_{2}}{T_{1}}\), where \(T_{1}\) is the source and \(T_{2}\) the sink temperature. Only these two temperatures appear, which is Carnot's theorem: every reversible engine working between the same two reservoirs has the same efficiency, whatever it uses.

Because both temperatures enter the formula, it depends on the source and on the sink together, not on one alone, and it certainly depends on them, which rules out the last option.

Answer: B

The incorrect statement is Change in the internal energy in a cyclic process is not zero.

Internal energy is a state function: it depends only on the state, so its change depends only on the initial and final states. In a cyclic process the system returns to its starting state, so \(\Delta U = 0\), the opposite of the chosen statement.

The others are correct: for an ideal gas \(U\) depends only on temperature; \(\Delta U\) depends only on the end states; and internal energy does depend on the state of matter (a phase change at constant temperature changes \(U\)).

Answer: C

The process is isothermal.

With \(\gamma = C_{p}/C_{v} = 1\), the equation \(PV^{\gamma}\) = constant becomes \(PV\) = constant, which is Boyle's law for an ideal gas at constant temperature.

An adiabatic process has \(PV^{\gamma}\) = constant with \(\gamma \gt 1\); an isobaric process is \(PV^{0}\) = constant (P constant); and an isochoric process corresponds to \(\gamma \to \infty\) (V constant). 'Irreversible' is not a value of the index at all.

Answer: A

The ratio is 3 : 4.

The rate of heat conduction through a section is \(H = kA\frac{\Delta T}{L}\), and the rod is uniform, so \(H\) is proportional to the temperature gradient:

\[ \begin{aligned} AB: \frac{100 - 80}{0.4} &= 50\ ^{\circ}\text{C m}^{-1} \\ BC: \frac{80 - 40}{0.6} &= \frac{200}{3}\ ^{\circ}\text{C m}^{-1} \\ \text{ratio} &= 50 : \tfrac{200}{3} = 3 : 4 \end{aligned} \]

Comparing temperature drops alone (20 : 40 = 1 : 2) ignores the different lengths, and 2 : 1 inverts that.

Answer: A

The temperature should be increased to 3T.

By Wien's displacement law, \(\lambda_{m}T\) is constant, so the peak wavelength is inversely proportional to the temperature:

\[ T' = T\cdot\frac{\lambda_{m}}{\lambda_{m}/3} = 3T \]

A shorter peak wavelength means a hotter body, so 'decreased' is wrong. 9T and \(\sqrt{3}\)T apply power laws that Wien's law does not contain.

For example, a star with peak emission at 1500 nm would need to be three times hotter for its peak to shift to 500 nm.

Answer: E

The heat withdrawn is 240 kcal.

Water and ice are both at \(0^{\circ}\)C, so only the latent heat of fusion is removed:

\[ Q = mL = 3 \times 80 = 240\ \text{kcal} \]

80 kcal is the amount for 1 kg, and 160, 320 and 400 kcal correspond to 2, 4 and 5 kg.

Removing the same heat from water already at 0°C changes its state without lowering its temperature; cooling to below 0°C would need the specific heat of ice as well, which this question does not involve.

Answer: B

The process is isothermal expansion.

By the first law, \(Q = \Delta U + W\). For an ideal gas the internal energy depends only on temperature, so at constant temperature \(\Delta U = 0\) and \(Q = W\): all the heat supplied becomes work. Work done on the surroundings means the gas expands.

In a compression the surroundings do work on the gas, and the gas gives out heat. In an adiabatic process no heat is supplied at all, and in an isobaric process part of the heat raises the internal energy.

Answer: D

Specific heat capacity depends on the material and temperature of the substance.

Specific heat capacity is heat per unit mass per degree, \(c = \frac{Q}{m\Delta T}\). Dividing by the mass makes it a property of the material, independent of how much there is. It also varies with temperature (it falls sharply at low temperatures, for instance), which is why tables quote it at a given temperature.

Mass and volume affect the total heat capacity of an object, not the specific heat, so the options naming mass or volume are wrong, and 'material only' leaves out the temperature dependence.

Answer: B

The incorrect statement is In an adiabatic process, there is a heat exchange with the surrounding.

An adiabatic process is defined by Q = 0: no heat enters or leaves the system, and any change in internal energy comes from work alone.

The other statements are the definitions of the processes: isochoric means constant volume, isobaric constant pressure, isothermal constant temperature. In a cyclic process the system returns to its initial state, and internal energy is a state function, so its change is zero.