Question

The volume V of a given mass of gas varies

directly as the temperature T and inversely as the
pressure P. If V = 341.0 in 3 when T = 310° and
P=10 lb/in.2, what is the volume when T= 120°
and P= 15 lb/in.2?

Answer 1

Apply combine gas law

`\\ \rm\dashrightarrow (P1V1)/(T1)=(P2V2)/(T2)`

`\\ \rm\dashrightarrow (10(341))/(310)=(15V2)/(120)`

`\\ \rm\dashrightarrow 11=(V2)/(8)`

`\\ \rm\dashrightarrow V2=88in^3`

Answer 2

88 in³

Explanation:

we are given that the volume V of a given mass of gas varies directly as the temperature T and inversely as the pressure P.

Condition-1:

The volume V of a given mass of gas varies directly as the temperature T , thus

`V\propto T\\\implies V=kT`

Condition-1:

The volume V of a given mass of gas varies inversely as the pressure P, therefore,

`V\propto 1/P\\\implies V=k\cdot 1/P`

combining 1 and 2 yields

`V\propto k\cdot T/P`

Case-1:

• V = 341.0 in³
• T = 310°
• P=10 lb/in²

To find:

• k

Finding the constant of proportionality

`341= k\cdot 310/10\\\implies k=341* 10/310 \\ \implies \boxed{k=11}`

Case-1:

To find:

• V

when:

• T = 120°
• P=15 lb/in²
• k=11

Finding the volume:

`V= 11* 120/15\\\implies V=11* 8 \\ \implies \boxed{V=88}`