What is the molar heat capacity for the process, when 10 J of heat added to a monoatomic ideal

step 1 Hello students. So in this question we have to calculate the molar heat capacity C of the proces

What is the molar heat capacity for the process, when 10 J...

What is the molar heat capacity for the process, when $10 \mathrm{~J}$ of heat added to a monoatomic ideal gas in a process in which the gas performs a work of $5 \mathrm{~J}$ on its surrounding?
(a) $2 R$
(b) $3 R$
(c) $4 R$
(d) $5 R$

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Key Concepts

Molar Heat Capacity

Molar heat capacity is defined as the amount of heat required to raise the temperature of one mole of a substance by one degree. It is determined by the ratio of the heat exchanged to the temperature change and depends on the specific process (e.g., constant volume, constant pressure, or another process path) along which the heat is added. This concept helps in characterizing the thermal response of a gas under different conditions.

Internal Energy of an Ideal Gas

For an ideal gas, particularly a monoatomic one, the internal energy depends solely on temperature and is given by a multiple of the temperature change. In the case of a monoatomic ideal gas, the internal energy change is expressed as (3/2) R times the change in temperature per mole, reflecting the degrees of freedom of the gas particles.

First Law of Thermodynamics

This principle states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. It provides a fundamental energy balance that connects heat, work, and internal energy and is essential for analyzing energy transfers in thermodynamic processes.

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