Answer:
24) W = 75 [J]; 25) W = 1794[J]; 26) n = 8.8 (times) or 9 (times)
Explanation:
24) This problem can be solved by means of the following equation.

where:
DU = internal energy difference [J]
Q = Heat transfer [J]
W = work [J]
Since there are no temperature changes the internal energy change is equal to zero
DU = 0
therefore:

The work is equal to the heat transfered, W = 75 [J].
25) The heat transfer can be calculated by means of the following equation.
![Q = m*c_{p}*DT\\where:\\m = mass = 0.4[kg]\\c_{p} = specific heat = 897[J/kg*K]\\DT= 5 [C]](https://tex.z-dn.net/?f=Q%20%3D%20m%2Ac_%7Bp%7D%2ADT%5C%5Cwhere%3A%5C%5Cm%20%3D%20mass%20%3D%200.4%5Bkg%5D%5C%5Cc_%7Bp%7D%20%3D%20specific%20heat%20%3D%20897%5BJ%2Fkg%2AK%5D%5C%5CDT%3D%205%20%5BC%5D)
Q = 0.4*897*5 = 1794[J]
Work is equal to heat transfer, W = 1794[J]
26) Each time the bag falls the potential energy is transformed into heat energy, which is released into the environment. In this way the potential energy is equal to the developed heat.

where:
m = mass = 0.5[kg]
g = gravity = 9.81[m/s^2]
h = 1.5 [m]
![E_{p}=0.5*9.81*1.5\\E_{p}=7.36[J]](https://tex.z-dn.net/?f=E_%7Bp%7D%3D0.5%2A9.81%2A1.5%5C%5CE_%7Bp%7D%3D7.36%5BJ%5D)
The heat developed can be calculated by means of the following equation.
![Q=m*c_{p}*DT\\Q=0.5*130*1\\Q=65[J]](https://tex.z-dn.net/?f=Q%3Dm%2Ac_%7Bp%7D%2ADT%5C%5CQ%3D0.5%2A130%2A1%5C%5CQ%3D65%5BJ%5D)
The number of times will be calculated as follows
n = 65/7.36
n = 8.8 (times) or 9 (times)
First change km/ s into m/s, then use the formula
Lambda = velocity/ frequency
Answer : The temperature of the hot reservoir (in Kelvins) is 1128.18 K
Explanation :
Efficiency of carnot heat engine : It is the ratio of work done by the system to the system to the amount of heat transferred to the system at the higher temperature.
Formula used for efficiency of the heat engine.

where,
= efficiency = 0.780
= Temperature of hot reservoir = ?
= Temperature of cold reservoir = 
Now put all the given values in the above expression, we get:



Therefore, the temperature of the hot reservoir (in Kelvins) is 1128.18 K