Under constant-volume conditions, 3500 J of heat is added to 1.6 moles of an ideal gas. As a res

step 1 3500 joules of heat is required to change the temperature of 1 .6 mole of a gas by 75 Kelvin at

Under constant-volume conditions, 3500 J of heat is added to...

Under constant-volume conditions, 3500 $\mathrm{J}$ of heat is added to 1.6 moles of an ideal gas. As a result, the temperature of the gas increases by 75 $\mathrm{K}$ . How much heat would be required to cause the same temperature change under constant-pressure conditions? Do not assume anything about whether the gas is monatomic, diatomic, etc.

Under constant-volume conditions, 3500 $\mathrm{J}$ of heat is added to 1.6 moles of an ideal gas. As a result, the temperature of the gas increases by 75 $\mathrm{K}$ . How much heat would be required to cause the same temperature change under constant-pressure conditions? Do not assume anything
about whether the gas is monatomic, diatomic, etc.

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Key Concepts

Heat Capacities (Cv and Cp)

Heat capacities are properties that indicate how much heat is needed to change an ideal gas's temperature by a given amount. At constant volume (Cv), all added heat increases the internal energy rather than doing work, while at constant pressure (Cp), some heat is expended in performing work to expand the gas. The relationship Cp = Cv + R, where R is the gas constant, encapsulates the extra energy required at constant pressure.

Constant-Volume Process

In a constant-volume process, the volume of the system remains fixed. Consequently, when heat is added, it entirely raises the internal energy of the gas since there is no work done from expansion. This process is described by the equation Q = nCv?T, linking the heat, number of moles, specific heat at constant volume, and the temperature change.

Constant-Pressure Process

A constant-pressure process maintains fixed pressure while allowing the volume to change. When heat is added under these conditions, the energy not only increases the internal energy of the gas but also performs work to expand the gas. The required heat is calculated with Q = nCp?T, reflecting the extra energy input compared to the constant-volume scenario.

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