One mole of an ideal gas requires 207 J heat to raise the...

One mole of an ideal gas requires 207 J heat to raise the temperature by $1 \mathrm{~K}$, when heated at constant pressure. If the same gas is heated at constant volume to raise the temperature by the same range, the heat required will be (Take $R=8.3 \mathrm{Jmol}^{-1} \mathrm{~K}^{-1}$ ) (a) $215.3 \mathrm{~J}$ (b) $198.7 \mathrm{~J}$ (c) $207 \mathrm{~J}$ (d) None of these

One mole of an ideal gas requires 207 J heat to raise the temperature by $1 \mathrm{~K}$, when heated at constant pressure. If the same gas is heated at constant volume to raise the temperature by the same range, the heat required will be (Take $R=8.3 \mathrm{Jmol}^{-1} \mathrm{~K}^{-1}$ )
(a) $215.3 \mathrm{~J}$
(b) $198.7 \mathrm{~J}$
(c) $207 \mathrm{~J}$
(d) None of these

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Key Concepts

Ideal Gas Behavior

This concept outlines the laws governing ideal gases, including how pressure, volume, and temperature are interrelated. It forms the basis for understanding processes such as constant pressure and constant volume heating and is encapsulated in equations like PV=nRT.

Heat Capacity at Constant Pressure (Cp) and Constant Volume (Cv)

Heat capacities are a measure of the amount of heat required to change the temperature of a substance. Cp is the heat capacity when a gas is heated at constant pressure and Cv at constant volume. For ideal gases, these capacities are related by the equation Cp - Cv = R, where R is the ideal gas constant.

Heat Transfer in Thermodynamic Processes

This concept deals with the relationship between the quantity of heat added to a system and the resulting change in its temperature, which is key in determining the energy requirements for various processes under different constraints such as constant pressure or constant volume.

Application of the Ideal Gas Constant (R)

R is a fundamental constant in the ideal gas law that also appears in the relation between Cp and Cv. It quantifies the difference in energy required to heat an ideal gas under constant pressure versus constant volume conditions.

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