I got 300 cubic cm but the answer is 308 on the answer sheet. How?

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2 Answers
Oct 15, 2017

Check below

Explanation:

Writing the equation using the first sentence, we get

V=kT/P, where k is a constant of proportionality.

Now, let's use the first set of values.

231 cm^3=k*(300K)/(20(lb)/(cm^2))

k=((231 cm^3) * (20(lb)/(cm^2)))/(300K)

k=15.4 (lb*cm)/(K)

Now, let's use the second set of values and the constant determined above.

V=15.4(lb*cm)/(K)*(320K)/(16(lb)/(cm^2))

V=308 cm^3

You may have rounded the 15.4 to 15 as an intermediate step. This is something I would refrain from doing; always round at the end of a question.

Another potential reason is that the values in the question to only have 1 significant digit. Thus, 308 would round to 300.

In either case, I think you got the idea behind the question, so you should be fine.

Oct 15, 2017

Yes answer is 308cm^3. For details see below.

Explanation:

As volume V of a given mass of gas varies directly as temperature T and inversely as pressure P, the relation between two states of the same mass of gas is

(P_1V_1)/(T_1)=(P_2V_2)/(T_2)

Here P_1=20(lb)/(cm)^2, V_1=231cm^3 and T_1=300^@K

and P_2=16(lb)/(cm)^2 and T_2=320^@K

Hence (20xx231)/300=(16xxV_2)/320

and V_2=(20xx231)/300xx320/16

= (20xx231)/300xxcancel320^20/cancel16^1

= (20xx231)/300xx20

= (20xx231)/cancel300^15xxcancel20^1

= (20xx231)/15=(20xx231)/(5xx3)

= (cancel20^4xxcancel231^77)/(cancel5^1xxcancel3^1)

= 4xx77=308