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Difficulty: Very hardHeat Capacity and Specific Heat Capacity

The specific heat capacity of a gas undergoing an isothermal expansion is zero because the temperature of the gas does not change during the process.

Answer: Answer

Answer

The statement is False. During an isothermal process, the specific heat capacity of a gas is infinitely large (∞\infty), not zero.
The statement is false because the specific heat capacity c=QmΔTc = \frac{Q}{m \Delta T} of a gas during an isothermal process (ΔT=0,Q≠0\Delta T = 0, Q \neq 0) is infinitely large (∞\infty). A specific heat capacity of zero occurs during an adiabatic process where no thermal energy enters or leaves the system (Q=0Q = 0) while temperature changes.

Step-by-Step Solution

1
Apply the fundamental defining equation for specific heat capacity.
c=QmΔTc = \frac{Q}{m \Delta T}, where QQ is the quantity of heat transferred, mm is the mass, and ΔT\Delta T is the change in temperature.
Specific heat capacity measures the amount of heat required per unit mass to produce a unit temperature change under a defined thermodynamic process.
2
Identify the thermodynamic boundary conditions for an isothermal expansion.
The temperature remains constant throughout the expansion, so ΔT=0\Delta T = 0, but heat energy Q>0Q > 0 must be supplied to offset the work done by the expanding gas.
According to the First Law of Thermodynamics, ΔU=Q−W\Delta U = Q - W. For an ideal gas undergoing an isothermal process, ΔU=0\Delta U = 0, which mandates Q=W≠0Q = W \neq 0.
3
Evaluate the limit of cc as ΔT→0\Delta T \to 0 for a non-zero heat input QQ.
c=Qm⋅0→∞c = \frac{Q}{m \cdot 0} \to \infty.
Dividing a finite non-zero quantity of heat by a zero temperature change yields an infinitely large heat capacity.
4
Contrast this result with the condition required for a specific heat capacity of zero.
For c=0c = 0, the heat input must be zero (Q=0Q = 0) while ΔT≠0\Delta T \neq 0, which defines an adiabatic process.
Zero heat capacity means temperature changes without any heat transfer.

Key Concept

Thermodynamic process dependence of specific heat capacity
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Topics

Heat Capacity and Specific Heat Capacity

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