a ) 19,536.72 J,
b ) ( About ) 84°C
a ) We can solve this problem assuming that the dishwater remains a constant 78°C the entire duration.
Q = mass of the glass specific heat of the glass
The mass of the glass is given by 401 g, the specific heat by 840 J / kg C. Respectively the change in temperature would be the difference between the temperature of the dishwater, and that of the glass. As we want the units in Joules, we need to first convert the 401 g ⇒ kilograms.
401 g = 401 / 1000 kg = 0.401 kg,
Q = 0.401 kg 840 J / kg 19,536.72 J
b ) We know that the specific heat capacity of water is 4.184 J / g C. As the final temperature will be common between each substance, we can make their respective heat absorbed, the same. Note that the heat capacity is given in J / g
0.023 kg = 0.023 1000 = 23 g,
0.18 kg = 180 g
The final temperature will be about 84°C
b would be the answer