Final answer:
To calculate the amount of heat needed to increase the temperature of an ideal monatomic gas, you can use the formula Q = nCΔT, where Q is the amount of heat, n is the number of moles of gas, C is the molar heat capacity, and ΔT is the change in temperature. For an ideal gas, the molar heat capacity at constant pressure (Cp) is 5/2R, and at constant volume (Cv) is 3/2R, where R is the ideal gas constant. Using this information, you can calculate the amount of heat needed when the pressure or the volume is held constant.
Step-by-step explanation:
The amount of heat needed to increase the temperature of an ideal monatomic gas can be calculated using the formula:
Q = nCΔT
where Q is the amount of heat, n is the number of moles of gas, C is the molar heat capacity, and ΔT is the change in temperature.
For an ideal gas, the molar heat capacity at constant pressure (Cp) is given by Cp = 5/2R, and at constant volume (Cv) is Cv = 3/2R, where R is the ideal gas constant.
So, to calculate the amount of heat needed to increase the temperature:
(a) If the pressure is held constant:
Q = nCpΔT = (5.5 mol)(5/2R)(27 K)
(b) If the volume is held constant:
Q =