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#