Chocolate begins to melt between 40°C and 45°C depending on the different components of chocolate. Assume that the melting temperature for chocolate is 43°C, and that heat transfer between the marshmallow and chocolate is perfectly efficient. Given this, to what temperature should you cool the roasted marshmallow (7.5 g) before adding it to the s'more so that the chocolate (50 g) is warmed up to 43°C from 25°C? Use 2 J/g⋅°C as the specific heat for both the chocolate and the marshmallow.
Enter the ideal temperature of the marshmallow in degrees Celsius
To solve this problem, we need to calculate the amount of heat exchange that occurs when the marshmallow is cooled and the chocolate is warmed up.
First, let's calculate the heat exchange for the chocolate using the equation:
Q = m * c * ΔT
where Q is the heat exchange, m is the mass, c is the specific heat, and ΔT is the change in temperature.
For the chocolate:
m = 50 g
c = 2 J/g⋅°C
ΔT = 43°C - 25°C = 18°C
Q_chocolate = 50 g * 2 J/g⋅°C * 18°C = 1800 J
Next, let's calculate the heat exchange for the marshmallow. Since the marshmallow needs to be cooled, we need to use a negative value for the change in temperature.
For the marshmallow:
m = 7.5 g (mass of marshmallow)
c = 2 J/g⋅°C
ΔT = T_final - T_initial
To find the ideal temperature of the marshmallow that will warm up the chocolate to 43°C, we know that the initial temperature of the marshmallow will be its final temperature after cooling.
Q_marshmallow = 1800 J
Using the equation Q = m * c * ΔT, we can solve for ΔT:
1800 J = 7.5 g * 2 J/g⋅°C * (T_final - T_final)
1800 J = 15 J/°C * T_final
T_final = 1800 J / 15 J/°C
T_final = 120°C
Therefore, you should cool the roasted marshmallow to approximately 120°C before adding it to the s'more to warm up the chocolate to 43°C.
where is your work? The sum of heats gained is zero.
Heatmarshmellow+heatchco=0
7.5*c*(Tf-Ti)+59*c*(Tf-25)=0
Tf=43
Ti is the temp you have cooled the marsmellow before adding choc
Solve.