Please show step by step work if possible e. A>E>B-D>CE is correct 7. A containe

Question

Please show step by step work if possible e. A>E>B-D>CE is correct 7. A container with a piston contains 0.25mol of a monatomic (d.o.f. 3) ideal gas is held over a flame. A force of 3200N is applied to the piston pushing it a distance of 0.125m At the beginning of the application of force, the temperature of the gas is 300K. During the duration of the push, 250J of energy entered the gas from the flame. What 0 is the temperature of the gas at the end of the push? a. 509 K b. 428 K C. 380 K d. 312 K e. 289 K A is correct

Explanation / Answer

dQ = dU + dW
Where dQ is the supplied heat energy, dQ = 250 J
dU is the change in internal energy, dU = nCv dT
Where n is the number of moles, Cv is the specific heat of monoatomic gas and dT is the increase in temperature.
Cv for monoatomic gas = 3/2 R, where R is the universal gas constant.
dW is the word done, dW = - F x d
= - 3200 x 0.125 = - 400 J            
dU = dQ - dW
= 250 - (-400) = 650 J
nCvdT = 650
0.25 x 3/2 x 8.314 x dT = 650
dT = 650/3.118
= 209 K
Tf - Ti = 209
Tf = 209 + Ti
= 209 + 300 = 509 K

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