Thermodynamics

A lead ball at 30°C is dropped from a height of 6.2 km. The ball is heated due to the air resistance and it completely melts just before reaching the ground. The molten substance falls slowly on the ground. If the specific heat of lead = 126 Jkg^-1 oC^-1 and melting point of lead= 130°C and suppose that any mechanical energy lost is used to heat the ball, then the latent heat of fusion of lead is

• 2.4 × 10⁴ J Kg^-1

• 3.6 × 10⁴ J Kg^-1

• 7.6 × 10² J kg^-1

• 4.94 × 10³ J kg^-1

The given p-V diagram shows gases during adiabatic process. Plots 1 and 2 should correspond respectively to

• He and O₂

• O₂ and He

• He and Ar

• O₂ and N₂

For an adiabatic expansion of a monoatomic perfect gas, the volume increases by 24%. What is the percentage decrease in pressure?

• 24%

• 40%

• 48%

• 71%

One mole of a monoatomic ideal gas undergoes the process A → B in the given p-V diagram. The molar heat capacity for this process is

• $\frac{3\mathrm{R}}{2}$

• $\frac{13 \mathrm{R}}{6}$

• $\frac{5 \mathrm{R}}{2}$

• 2R

A lead bullet penetrates into a solid object and melts. Assuming that 50% of its kinetic energy was used to heat it, the initial speed of the bullet is (the initial temperature of the bullet is 25^oC and its melting point is 300°C). Latent heat of fusion of lead= 2.5 x 10⁴ J/kg and specific heat capacity of lead= 125 J/kg-K

• 100 m/s

• ≈ 490 m/s

• 520 m/s

• 360 m/s

The slope of isothermal and adiabatic curves are related as

• isothermal curve slope= adiabatic curve slope

• isothermal curve slope = γ × adiabatic curve slope

• adiabatic curve slope = γ× isothermal curve slope

• adiabatic curve slope =$\frac{1}{2}$× isothermal curve slope

The volume of an ideal gas is doubled in an isothermal process. Then, which of the following is true?

• Work done by the gas is positive

• Work done by the gas is negative

• Internal energy of the system decreases

• Internal energy of the system increases

When an ideal monoatomic gas is heated at constant pressure, the fraction of the heat energy supplied which increases the internal energy of the gas is

• 2 / 5

• 3 / 5

• 3 / 7

• 5 / 7

A Carnot engine operates with source at 127°C and sink at 27°C. If the source supplies 40 kJ of heat energy, the work done by the engine is

• 30 kJ

• 10 kJ

• 4 kJ

• 1 kJ

Assertion:  The specific heat of a gas in an adiabatic process is zero and in an isothermal process is infinite.

Reason:  Specific heat of gas is directly proportional to change of heat in system and inversely proportional to change in temperature.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false.