Question

A bubble of 6.00 mol helium is submerged at a certain depth in liquid water when the water ( and thus the helium ) undergoes a temperature increase T of 20 C at constant pressure. As a result, the bubble expands. (a) How much heat Q is added to the helium during the expansion and temperature increase? (b) What is the change Eint in the internal energy of the helium during the temperature increase? (c) How much work W is done by the helium as it expands against the pressure of the surrounding water during the temperature increase?

Answer #1

(a) How much heat Q is added to the helium during the expansion and temperature increase?

using a formula, we have

Q = n C_{p}T

For any ideal gas, C_{p} = C_{v} +
R

Q = n (C_{v} + R) T

where, C_{v} = (3/2) R

THEN, we get

Q = n [(1.5) R + R] T

Q = (6 mol) (2.5) (8.314 J/mol.K) (20 ^{0}C)

**Q = 2494.2 J**

(b) What is the change, E_{int} in the internal energy
of the helium during the temperature increase?

using a formula, we have

E_{int} = n C_{v}T = n (1.5 R)
T

E_{int} = (6 mol) (1.5) (8.314 J/mol.K) (20
^{0}C)

**E _{int} = 1496.5 J**

(c) How much work W is done by the helium as it expands against the pressure of the surrounding water during the temperature increase?

we know that, W = n R T

W = (6 mol) (8.314 J/mol.K) (20 ^{0}C)

**W = 997.6 J**

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