It sounds like you need to find out how the pressure of the air trapped in the woman's lungs will be affected by the temperature change as the air warms. It appears that you are to assume that the air will reach her body temperature of 37ºC during the time that she holds her breath.
Since there is a fixed number of moles of gas at constant volume, the pressure will vary directly with the Kelvin temperature. We can use the gas law equation that relates pressure and temperature:
`P_1/T_1 = P_2/T_2`
Here's the information you're given:
P1 = 1.08 atm
T1 = (20ºC + 273) = 293 Kelvins
T2 = (37ºC + 273) = 310 Kelvins
Rearrange the equation to isolate P2:
`P_2 = [(P_1)(T_2)]/(T_1)`
P2 = (1.08 atm)(310 K)/(293 K) = 1.14 atm
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