please write the steps for these three quetions. thanks 1. In an adiabatic compr

Question

please write the steps for these three quetions. thanks

1. In an adiabatic compression of 1 mol of an ideal gas with Cv,m = 5R/2, the
temperature rises from 293 K to 325 K. Calculate q, w, deltaU, and deltaH for this
process.

2. 2.50 moles of an ideal gas for which CV,m = 20.8 J K-1 mol-1 is heated from
an initial temperature of 10.5 oC to a final temperature of 305 oC at constant
volume. Calculate q,w, deltaU, and deltaH for this process.

3. A 25.0-g sample of copper at 363 K is placed in 100.0 g of water at 293 K.
The copper and water quickly come to the same temperature by the process
of heat transfer from copper to water. Calculate the final temperature of
water. The molar heat capacity of copper is 24.5 J K-1 mol-1 and that of
water is 75.2 J K-1 mol-1.

Explanation / Answer

(1) In an adiabatic compression, heat transfer to the system = 0 Thus q = 0 q = W + deltaU = 0 deltaU = n * Cv * (Tf - Ti) = 1 * 5R/2 * (325 - 293) = 665.12 J W = - deltaU = - 665.12 J H = U + PV deltaH = deltaU + nR deltaT = 665.12 + ( 1 * 8.314 * (325-293) ) = 931.168 J (2) w = P * deltaV Constant volume --- deltaV = 0 W = P * 0 = 0 q = deltaU = n * Cv * deltaT = 2.5 * 20.8 * (305 - 105) = 10400 J deltaH = 10400 + ( 2.5 * 8.314 * (305 - 105) ) = 14557 J (3) Let the final temperature be T Heat transferred from Copper = Heat recieved by water Mc * Sc * (363 - T) = Mw * Sw * (T - 293) 363 - T = 12.277 (T - 293) 13.277 T = 3960 T = 298.277 K

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