Grams and volume of steam needed to raise the temperature of expresso

[merbear]

[SOLVED] Grams and volume of steam needed to raise the temperature of expresso

Homework Statement

The temperature of espresso coffee (mostly water) can be increased by blowing 100°C steam into it. How much steam (in grams) is needed to heat up a 13 cm3 cup of espresso from 46°C to 82°C? What is the volume of this quantity of steam, assuming that the steam is an ideal gas

Homework Equations

Q=mcdeltaT

dq=Cv*dt

The Attempt at a Solution

I know that the specific heat- amount of heat needed to raise the temperature 1 degree -is 4.186 J/gC. But I really don't have any idea as to how to start the problem. I tried using Q=mcdeltaT, but I don't have a value for Q.

I would appreciate any help in getting started. Thank you.

 

[member 553083]

Solution:We can use the equation Q = mcΔT to solve for the mass of steam needed. The heat required to raise the temperature from 46°C to 82°C is given by Q = (13 cm3) (4.186 J/g°C) (82°C - 46°C) = 524.5 J. Thus, the mass of steam needed is m = 524.5 J / (100°C - 46°C) (4.186 J/g°C) = 4.38 g.The volume of this quantity of steam can be calculated using the ideal gas law, PV = nRT, where n is the number of moles of steam and R is the ideal gas constant, which has a value of 8.314 J/molK. We can rearrange the equation to calculate the volume of steam as V = nRT/P = (4.38 g)(8.314 J/molK)(273.15 K)/(1.01325 x 105 Pa) = 0.11 L.