Question

You mix 5 moles of H2 at 300 K with 5 moles of He at 360 K in a perfectly insulated calorimeter. Is the final temperature higher or lower than 330 K?

(a) Higher
(b) Lower
(c) Equal to 330 K
(d) None of these

Answer 1

Using the principle of energy conservation and the specific heat capacities of the gases, we can determine the final temperature of the mixture.

Step-by-step explanation:

In this case, we can use the principle of energy conservation to determine whether the final temperature is higher or lower than 330 K. Since the calorimeter is perfectly insulated, no heat is gained or lost to the surroundings. Therefore, the total energy of the system is constant.

Using the formula:

m1c1ΔT1 + m2c2ΔT2 = 0

Where:

m1 and m2 are the moles of each gas

c1 and c2 are the specific heat capacities of each gas

ΔT1 and ΔT2 are the changes in temperature of each gas

We can substitute the values into the equation:

(5 mol)(4.184 J/g°C)(T - 300 K) + (5 mol)(4.184 J/g°C)(T - 360 K) = 0

Simplifying the equation:

5(T - 300) + 5(T - 360) = 0

10T - 1500 - 1800 = 0

10T = 3300

T = 330 K

Therefore, the final temperature is equal to 330 K, so the answer is (c) Equal to 330 K.