The temperature of 2.97 mol of a monatomic ideal gas is 511 K. The internal energy of this gas is doubled by the addition of heat. How much heat is needed when it is added at (a) constant volume and (b) constant pressure

The heat needed when volume is constant is 18926.9 J

The heat needed when pressure is constant is 31544.8 J

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