A large closed bag of plastic contains 0.10 m 3 an unknown gas at an initial tem

Question

A large closed bag of plastic contains 0.10 m3 an unknown gas at an initial temperature of 10 degree Celsius and at the same pressure as the surrounding atmosphere, 1.0 atm. You place this bag in the sun and let the gas warm up to 38 degree Celsius and expand to .11 m3 . During this process, the gas absorbs 840 cal of heat. Assume the bag is large enough so the gas never strains against it, and therefore remains at a constant pressure of 1.0 atm.

a) How many moles of gas are in the bag?

b) What is the work done by the gas in the bag against the atmosphere during the expansion?

c) What is the change in the internal energy of the gas in the bag?

d) Is the gas a monoatomic gas? A diatomic gas?

I know this deals with the 1st Law of Thermodyanmics, just not sure how to apply to the equations. Thanks.

Explanation / Answer

a) PV = nRT
1* 0.1*1000 = n* 0.0821 * (273 + 10)
n=4.303981 moles
b)
work done = P * ( v2-v1) = 101325* (0.11- 0.1) = 1013.25 J = 242.172562 cal.
c)
change in the internal energy of the gas in the bag = q- W = 840 - 242.172562 = 597.8274 cal. = 2501.3098430 J
d)
for monoatomic gas,
change in the internal energy of the gas in the bag = 1.5 * n* R* ( T2-T1) = 1.5 * 4.303981 * 8.314 * ( 38 - 10) = 1502.898517428 J
for diatomic gas,
change in the internal energy of the gas in the bag = 2.5 * n* R* ( T2-T1) = 2.5 * 4.303981 * 8.314 * ( 38 - 10) = 2504.83086238 J
so the gas is diatomic.

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