specific heat to energy or temp

Question

A. In the laboratory a student finds that it takes 3.05×10³ Joules to increase the temperature of 14.9 grams of gaseous hydrogen from 21.3 to 36.8 degrees Celsius.

The specific heat of hydrogen he has measured is  J/g°C.

B. A sample of gaseous hydrogen is heated with an electrical coil. If 2.58×10³ Joules of energy are added to a 11.8 gram sample initially at 21.0 °C, what is the final temperature of the hydrogen?

Answer must be in C.

Answer 1

Hello, Natalie,

Use the units (and definition) of specific heat to guide you to the solution. In this case, specific heat is defined as the amount of energy (Joules) it takes to raise 1 gram of the material (H2) by 1 degree C: J/g°C. I say "in this case<" since specific heat can be expressed in many different units. Take your pick. Energy can be in calories, Btu, kJ, and so on. The unit of material can be grams, kg, moles, ml, etc.. Temperature is often in C, but K and F may also appear.

At any rate, we have J/g°C. We are given that the gaseous hydrogen requires 3.05×10³ Joules to increase the temperature of 14.9 grams from 21.3 to 36.8 degrees Celsius. Simply place these numbers in the format (3.05×10³ J)/(14.9 g)*(36.8 - 21.3 C).

Calcule the result and note the the resulting unit is J/g°C, just what we wanted.

For Part B, use the equation relating heat, specific heat, temperature and mass:

q = cmDt, where q is the energy (Joules, here), c is the specific heat (calculated above), m is the mass (11.8 grams), and Dt is the temperature change, in this case (FinalT - 21C). Enter the data and then solve for FinalT,

I hope this helps, Bob