70 calorie of heat are required to raise the temperature of...

70 calorie of heat are required to raise the temperature of 2 mole of an ideal gas at constant pressure from $30^{\circ} \mathrm{C}$ to $35^{\circ} \mathrm{C}$ The amount of heat required to raise the temperature of the same gas through the same range at constant volume is $\ldots \ldots \ldots \ldots \ldots .$ calorie. (A) 50 (B) 30 (C) 70 (D) 90

Key Concepts

Constant Pressure Process

In thermodynamics, a constant pressure process (or isobaric process) is one in which the pressure remains unchanged. For an ideal gas undergoing such a process, the heat added is used both to increase the internal energy of the gas and to do work against the external pressure, which is expressed by the relation Q = n·C?·?T.

Constant Volume Process

A constant volume process (or isochoric process) is a thermodynamic process where the volume remains fixed. In this case, no work is done by the system, so the entire heat supplied goes into changing the internal energy of the gas, following the equation Q = n·C?·?T.

Molar Heat Capacities

Molar heat capacities are the amounts of heat required to raise the temperature of one mole of a substance by one degree. For ideal gases, these are defined at constant pressure (C?) and constant volume (C?), and they quantify the energy needed to achieve a unit change in temperature under different constraints.

Mayer's Relation

Mayer's relation provides a fundamental connection between the molar heat capacities of an ideal gas at constant pressure and constant volume. It states that C? = C? + R, where R is the universal gas constant. This relation helps in determining one heat capacity when the other is known, thus linking the energy changes in constant pressure and constant volume processes.

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