Question

A substance has a molar specific heat,c_vm=4.00Jk^-1mol^-1 and a molar mass, M=10.0g/mol. A 100.0g sample of this substance (sample 1) was cooled to 250*K, while a 1.000kg sample of the same substance (sample 2) was heated to 400.0*K. Assume that for temperatures between 250.0*K and 400.0*K, the substance remains the same thermodynamic phase, i.e. no phase transition takes place

A) suppose that both samples have been enclosed by adiabatic, rigid, impermeable walls andd then plaed next to each other. The samples are then observed one week later.

1) what are the temperatures of samples 1 and 2

2) how much energy has been transferred as heat into sample 1? into sample 2?

3) how much work was done on sample 1? On sample 2?

4) what is the change in internal energy for sample 1? For sample 2?

B) Suppose that the wall separating the two samples is now made diathermal, but remains impermeable and rigid. Suppose that the two samples form an isolated system. The samples are then observed one week later.

1) what are the temperatures of samples 1 and 2

2) how much energy has been transferred as heat into sample 1? into sample 2?

3) how much work was done on sample 1? On sample 2?

4) what is the change in internal energy for sample 1? For sample 2?

Answer 1

C_vm = 4.00 JK^-1mol^-1  

Molar mass = 10.0 g/mol

For sample 1:

Mass = 100 g

Moles of substance = 100.0 / 10 = 10

Initial temperature = 250 K

For sample 2:

Mass = 1.0 kg = 1000 g

Moles of sample = 1000 / 10 = 100

Initial temperature = 400 K

1). Let the temperature of the samples be T.

Heat absorbed by sample 1 = Heat released by sample 2

m1* C* T1 = m2* C* T2

10 * 4 * (T - 250) = 100 * 4 * (400 - T)

T - 250 = 10 (400 - T)

T - 250 = 4000 - 10T

11T = 4250

T = 386.36 K

Temperature of sample 1 = sample 2 = 386.36 K

2). q1 = q2 = m1* C* T1

= 10 * 4 * (386.36 - 250)

= 5454.4 J

= 5.45 kJ