A frictionless piston-cylinder device and a rigid tank contain 3 kmol of an ideal gas at the sam

step 1 Our question is a frictionless piston cylinder device has a rigid tank contained 3 kilo mole of

A frictionless piston-cylinder device and a rigid tank...

A frictionless piston-cylinder device and a rigid tank contain $3 \mathrm{kmol}$ of an ideal gas at the same temperature, pressure, and volume. Now heat is transferred, and the temperature of both systems is raised by $10^{\circ} \mathrm{C}$. The amount of extra heat that must be supplied to the gas in the cylinder that is maintained at constant pressure is (a) $0 \mathrm{~kJ}$ (b) $27 \mathrm{~kJ}$ (c) $83 \mathrm{~kJ}$ (d) $249 \mathrm{~kJ}$ (e) $300 \mathrm{~kJ}$

A frictionless piston-cylinder device and a rigid tank contain $3 \mathrm{kmol}$ of an ideal gas at the same temperature, pressure, and volume. Now heat is transferred, and the temperature of both systems is raised by $10^{\circ} \mathrm{C}$. The amount of extra heat that must be supplied to the gas in the cylinder that is maintained at constant pressure is
(a) $0 \mathrm{~kJ}$
(b) $27 \mathrm{~kJ}$
(c) $83 \mathrm{~kJ}$
(d) $249 \mathrm{~kJ}$
(e) $300 \mathrm{~kJ}$

Key Concepts

First Law of Thermodynamics

The first law, which is a statement of energy conservation, applies to all processes and indicates that the change in internal energy of a system equals the heat added to the system minus the work done by it. This principle is fundamental in analyzing energy interactions in different thermodynamic processes, thereby highlighting why extra heat is needed when work is done during expansion at constant pressure.

Heat Capacities at Constant Pressure and Constant Volume

Heat capacitors, specifically Cp and Cv, indicate how much heat is required to raise the temperature under constant pressure and constant volume conditions respectively. For an ideal gas, the difference between Cp and Cv (which equals the gas constant, R) is crucial in quantifying the additional heat needed in a constant pressure process compared to a constant volume process.

Ideal Gas Behavior

This concept refers to the use of the ideal gas law, which relates pressure, volume, and temperature for an ideal gas. It provides a simplified model that allows for direct proportionalities and easy calculations when the gas undergoes changes in state, such as a temperature increase.

Constant Pressure Process

In a constant pressure process, the pressure remains fixed while the substance can expand or contract. The extra energy supplied as heat not only raises the temperature (and thus the internal energy) but also performs work as the gas expands. This distinguishes it from constant volume processes where no expansion work is done.

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