Answer:
The heat needed when volume is constant is 18926.9 J
The heat needed when pressure is constant is 31544.8 J
Step-by-step explanation:
Step 1: Data given
Number of moles of a monoatomic gas = 2.97 mol
Temperature of the gas = 511 K
The internal energy of this gas is doubled by the addition of heat.
Step 2:
At a constant volume workdone is 0.
Q = ΔU + W
Q = 3/2 n*R*T
⇒n = the number of moles = 2.97 moles
⇒R = the gas constant = 8.314 J/mol*K
⇒with T = the temperature = 511 K
Q = 3/2 *2.97 * 8.314 * 511
Q = 18926.9 J
Step 3: At a constant pressure workdone is:
W = p*V
W = n*R*T
⇒ Q = ΔU + W
Q = 3/2 *nRT + nRT
Q = 18926.9 + 2.97 * 8.314 * 511
Q = 31544.8 J
The heat needed when volume is constant is 18926.9 J
The heat needed when pressure is constant is 31544.8 J