The mechanical equivalent of heat is 4.2 J/cal. Assuming no losses, the height from which a 1-g mass must fall

Question

in order to raise the temperature of 2 grams of water 1 C is approximately _____ (Hint: P.E. = mgh and H = mc T)

Answer 1

PE = mgh
H = mcT (for water, c = 1 cal/gC)

Step 1: Since you're finding an equivalent, these two formulas are equal to each other. Substitute the values given:
mgh = mcT
1g * 9.8 m/s^2 * h = 2g * 1 cal/gC * 1 C

Step 2: Simplify. Convert g to kg to let you combine the mass and gravitational acceleration to get Newtons. Mulitply the calories on the left side by the conversion factor between J and cal (4.2 J/cal)
1g * 9.8 m/s^2 * h = 2g * 1 cal/gC * 1 C
.001kg * 9.8 m/s^2 * h = 2 cal
.0098N * h = 2 cal * 4.2 J/cal
.0098N * h = 8.4 J

Step 3: Divide both sides by .0098N to find h.
.0098N * h = 8.4 J
h = 8.4 J /.0098N
h = 857 m (solution)