Five moles of a monatomic ideal gas expand adiabatically, and its temperature decreases from 410 to 200 K.

(a) What is the work done by (or done to) the gas? Include the algebraic sign.
J

(b) What is the change in the internal energy of the gas? Include the algebraic sign.
J

a. w = _ 13094,55 b. e = _ 13094,55

To find the work done by (or done to) the gas during an adiabatic expansion, you can use the first law of thermodynamics, which states that the change in internal energy of the gas is equal to the work done on the gas.

(a) The work done by (or done to) the gas can be calculated using the equation:

W = ΔU

In this case, since the process is adiabatic (i.e., no heat exchange occurs), the change in internal energy (ΔU) is equal to the work done (W) on the gas.

Therefore, to calculate the work done by (or done to) the gas, you need to determine the change in internal energy. The change in internal energy (ΔU) can be calculated using the equation:

ΔU = (3/2)nR(ΔT)

where n is the number of moles of the gas, R is the ideal gas constant, and ΔT is the change in temperature.

Given:
n = 5 moles
R = 8.314 J/(mol·K)
ΔT = 200 K - 410 K = -210 K (taking the sign into account)

Substituting these values into the equation:

ΔU = (3/2)(5)(8.314)(-210)

Calculating:

ΔU = -1572.3 J

Therefore, the change in internal energy of the gas is -1572.3 J. This means the internal energy decreased.

Since ΔU is equal to the work done (W), the work done by (or done to) the gas is also -1572.3 J.

Hence, the answer to part (a) is -1572.3 J.

(b) The change in internal energy of the gas is -1572.3 J (as calculated in part (a)).