Question

The temperature, T , of a given mass of gas varies inversely with its volume, V . The temperature of a certain gas with volume of 105 cm 3 is 30º C. What will be the temperature of the gas when it is compressed to a volume of 84 cm 3? 18.8º C 48º C 24º C 37.5º C

Answer 1

The temperature of a gas can be calculated using the formula for inverse variation, which is T1*V1 = T2*V2. By substituting the given values into the formula, we can find that the temperature of the gas when it is compressed to a volume of 84 cm^3 is 37.5ºC.

Step-by-step explanation:

To solve this problem, we can use the formula for inverse variation:

T1*V1 = T2*V2

Given that T1 = 30ºC, V1 = 105 cm^3, and V2 = 84 cm^3, we can solve for T2:

T2 = (T1*V1)/V2 = (30*105)/84 = 37.5ºC

Therefore, the temperature of the gas when it is compressed to a volume of 84 cm^3 will be 37.5ºC.

Answer 2

we know that

if the temperature T of a given mass of gas varies inversely with its volume V
then
T=k/V

Step 1
Find the value of k
for T=30º C and V=105 cm³
we have
T=k/V--------> k=T*V--------> k=30*105=3150 °C*cm³

therefore
for V=84 cm³
T=3150/84=37.5 °C

the answer is 37.5 °C