Question

II Review Part A Find the work done by a monatomic ideal gas as it expands from point A to point C along the path shown in the figure(Figure 1). Express your answer using two significant figures. W= = 2.6 MJ Figure < 1 of 1 Submit Previous Answers Correct B 600 Pressure, P (kPa) 400 Part B 200 If the temperature of the gas is 250 K at point A, what is its temperature at point C? Express your answer using two significant figures. 2. 4 8 10 Volume, V (m) Tc 1200 K

Answer 1

Answer:

Using part (A) and (B) answers,

Work done W = 2.6 x 10⁶ J

T_A = 250 K and T_C = 1200 k, so $\Delta$ T = 1200 K - 250 K = 950 K

The change in the internal energy of the system during the expansion is dU = nc_v$\Delta$T

Here n = 1 mol and c_v = 3/2 R (for monatomic gas), where R is gas constant and its value is 8.314 J.K^-1.mol^-1

Thus, dU = (1 mol) (3/2)(8.314 J.K^-1.mol^-1) (950 K) = 11847.45 J

According to first law of Thermodynamics,

dU = Q + W

or Q = dU - W

where Q is the amount heat added or removed from the gas during the expansion process.

Therefore, Q = 11847.45 J - 2.6 x 10⁶ J = -2.58 x 10⁶

The minus sign indicates that the energy is added to the gas

Hence, | Q | = 2.58 MJ