The volume of a gas decreases from 15.7 mºto 11.2 m3 while the pressure changes from 1.12 atm to 1.67 atm. If the initial temperature is 245 K, what is the final temperature of the gas?
O 117 K
230 K
261K
.
O 512K

Approximately , if this gas is an ideal gas, and that the quantity of this gas stayed constant during these changes.

Explanation:

Let and denote the pressure of this gas before and after the changes.

Let and denote the volume of this gas before and after the changes.

Let and denote the temperature (in degrees Kelvins) of this gas before and after the changes.

Let and denote the quantity (number of moles of gas particles) in this gas before and after the changes.

Assume that this gas is an ideal gas. By the ideal gas law, the ratios and should both be equal to the ideal gas constant, .

In other words:

.

.

Combine the two equations (equate the right-hand side) to obtain:

.

Rearrange this equation for an expression for , the temperature of this gas after the changes:

.

Assume that the container of this gas was sealed, such that the quantity of this gas stayed the same during these changes. Hence: , .

.