A glass beaker of unknown mass contains 65.0 mL of water.The system absorbs 2000.0 cal of heat and the temperature rises 20.0ºC as a result.What is the mass of the beaker? (The specific heat for glass is .18 cal/g · ºC. )
A)190 g
B)560 g
C)540 g
D)270,000 g

Question

Quizplus · Accepted Answer

First, calculate the amount of heat needed to raise the temperature of the water:
Q = m × c × ΔT
Q = (65.0 g × 1 mL/g) × (1 cal/g · ºC) × (20.0ºC)
Q = 13,000 cal

Since the system absorbs 2000.0 cal of heat in total, the rest of the heat (11,000 cal) must be absorbed by the beaker. We can use the same formula to calculate the mass of the beaker:
m = Q / (c × ΔT)
m = (11,000 cal) / (.18 cal/g · ºC × 20ºC)
m = 3055.56 g, or 3055.56 mL

However, we know that the beaker cannot weigh more than the total mass of water and itself. The density of water is 1 g/mL, so the mass of 65.0 mL of water is simply 65.0 g. Therefore, the mass of the beaker must be less than:
3055.56 g - 65.0 g = 2990.56 g

Choice A (190 g) is the only option that falls within this range.

A Glass Beaker of Unknown Mass Contains 65