Question

a) Calculate the change in entropy on heating an ideal gas from 300K to 500K at constant pressure.

b) Calculate the change in entropy on heating an ideal gas from 300K to 500K at constant volume.

c) why these answers are different.

Please explain each steps.

Answer 1

1.

First, we need to find the quantity of heat released from gold.

q = ∆T * Cp * m

Where q is quantity of heat, ∆T is difference between initial and final temperature, Cp is heat capacity and m is mass of gold.

q = (120-10) * 0.131 * 200 = 2882 J

Now we will calculate the how many degrees, 2882 J can increase of water.

We will use the same formula,

We know q, Cp and m and need to calculate ∆T

∆T = q/Cp*m = 2882/(4.184*25) = 27.55 degrees

So final temperature will be initial temp + 27.55 = 37.55 degree Celsius.

2.

Entropy change for the gold block. We will need to convert °C to K

∆S = m∙Cp∙ln(T_final/T_initial)

      = 200 * 0.131 * ln(37.55+273.15)K / (120+273.15)K

      = 200 * 0.131 * ln(310.7)K / (393.15)K

∆S = -6.166 J/K

3.

Entropy change of water. We will need to convert °C to K

∆S = m∙Cp∙ln(T_final/T_initial)

      = 25 * 4.184 * ln(37.55+273.15)K / (10+273.15)K

      = 25 * 4.184 * ln(310.7)K / (283.15)K

∆S = 9.712 J/K