How much heat does it take to increase the temperature of 1.80 mol of an ideal gas by 50.0 K near room temperature if the gas is held at constant volume and is (a) diatomic;
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1
Identify the specific heat capacity at constant volume for a diatomic gas. For diatomic gases near room temperature, the molar specific heat capacity at constant volume, $C_V$, is typically about 5R/2, where R is the universal gas constant (approximately 8.314 J/mol·K).
Calculate the total heat required using the formula $Q = nC_V\Delta T$, where $Q$ is the heat added, $n$ is the number of moles of the gas, $C_V$ is the molar specific heat capacity at constant volume, and $\Delta T$ is the change in temperature.
Substitute the given values into the formula: $n = 1.80$ mol, $C_V = \frac{5}{2}R$, and $\Delta T = 50.0$ K.
Perform the multiplication to find the value of $Q$. Remember to use the value of R as 8.314 J/mol·K.
The result from the calculation will give you the amount of heat in joules required to increase the temperature of the gas by 50.0 K at constant volume.