How much heat does it take to increase the temperature of 1.80 mol of an ideal gas by 50.0 K n

step 1 So how much heat does it take to increase the temperature of 1 .8 mole of an ideal gas by 50 deg

How much heat does it take to increase the temperature of...

How much heat does it take to increase the temperature of $1.80 \mathrm{~mol}$ of an ideal gas by $50.0 \mathrm{~K}$ near room temperature if the gas is held at constant volume and is (a) diatomic;
(b) monatomic?

Key Concepts

Constant Volume Process

In thermodynamics, a constant volume process means that the volume of the gas remains fixed while it is heated. Since no work is done by or on the gas (because work is volume change multiplied by pressure), the heat added goes entirely into increasing the internal energy of the gas.

Heat Capacity at Constant Volume (Cv)

The molar heat capacity at constant volume (Cv) is the amount of heat required to raise the temperature of one mole of a substance by one Kelvin at constant volume. For an ideal gas, the heat added can be calculated using the equation Q = n * Cv * ?T, where n is the number of moles and ?T is the change in temperature.

Degrees of Freedom

The degrees of freedom of a gas molecule dictate its capacity to store energy. Monatomic gases, which have only translational degrees of freedom, have a lower Cv (about 3/2 R), whereas diatomic gases have additional rotational degrees of freedom that add to their heat capacity, typically leading to Cv values around 5/2 R near room temperature.

Ideal Gas Behavior

The ideal gas model assumes that the molecules have no intermolecular forces and that the size of the molecules is negligible compared to the distance between them. This allows for simplified relations between pressure, volume, temperature, and energy, and is particularly useful when calculating heat changes in processes such as constant volume heating.

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