Question

15 point question

The pressure P of a gas varies inversely as its
volume V and directly as the temperature T. A
certain gas has a pressure of 2.7 atm, a
volume of 3.6 L, and a temperature of 324 K.
If the volume of the gas is kept constant and
the temperature is increased to 396 K, what
will the new pressure be?

Answer 1

The new pressure of the gas, when the volume is kept constant and the temperature is increased, is 1.23 atm.

Step-by-step explanation:

According to the problem, the pressure of a gas varies inversely as its volume and directly as the temperature. This means that as the volume decreases, the pressure increases, and as the temperature increases, the pressure also increases.

Given that the initial pressure (P) is 2.7 atm, the initial volume (V) is 3.6 L, and the initial temperature (T) is 324 K.

We can use the formula P = k * (1/V) * T, where k is a constant, to solve for the constant k.

Substituting the initial values into the formula, we get 2.7 = k * (1/3.6) * 324.

Solving for k, we find k = 0.222.

Now, since the volume is kept constant at 3.6 L and the temperature is increased to 396 K, we can use the formula

P = k * (1/V) * T to find the new pressure (P) as follows:

P = 0.222 * (1/3.6) * 396

= 1.23 atm.

Answer 2

The new pressure P₂ is 3.3 atm

Step-by-step explanation:

Pressure of gas = 2.7 atm

Volume = 3.6 L

Temperature = 324 K

Now we are given that volume of the gas is kept constant.

Temperature is increased to 396 K

We need to find the pressure.

The formula used is:
`(P_1)/(T_1)=(P_2)/(T_2)`

We have P₁ = 2.7

T₁ = 324 K

T₂ = 396 K

P₂ = ?

Putting values in the formula and finding P₂

`(P_1)/(T_1)=(P_2)/(T_2)\\(2.7)/(324)=(P_2)/(396)\\P_2=(2.7)/(324)* 396\\P_2=0.0083 * 396\\P_2=3.3`

So, the new pressure P₂ is 3.3 atm