Five moles of an ideal gas expands isothermally at 100 $\degree$C to five times its initial volume.Find the heat flow into the system. A)2.5 * 10⁴ J B)1.1 *10⁴ J C)6.7 * 10³ J D)2.9 *10³ J E)7.0 *10² J

Question

Quizplus · Accepted Answer

Since the process is isothermal, we know that ΔT = 0 and thus ΔU = 0. Therefore, the heat flow into the system (Q) is equal to the work done (W):

W = -PΔV

Where ΔV is the change in volume and P is the pressure of the gas.

From the ideal gas law, we know that PV = nRT, where n is the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin. Since the process is isothermal, T is constant and PV = nRT = constant.

When the gas expands to five times its initial volume, the final pressure (P2) is one-fifth of the initial pressure (P1):

P2 = P1/5

Thus, the work done is:

W = -PΔV = -∫PdV = -∫(nRT/V)dV = -nRTln(V2/V1)

= -(5 mol)(8.314 J/mol K)(373.15 K)ln(5) = -44,310.65 J = -(44.31 kJ)

Since the work done is negative (since the gas is expanding), the heat flow into the system is positive:

Q = 44.31 kJ = 2.5×10^4 J = 2.5 kJ (to 2 significant figures)

Therefore, the best choice is A: 2.5×10^4 J.

Five Moles of an Ideal Gas Expands Isothermally at 100 °\degree°

Five Moles of an Ideal Gas Expands Isothermally at 100 $\degree$