Heat Capacity energy exchange problem

[sww_world]

Homework Statement

Mr. Gryphon was taking a break between classes and decided to make himself a cup of tea. He poured 250g of water at 95°C into an 85g porcelain mug which had an initial temperature of 19°C. What was the final temperature of the water for his tea? ( Not technically part of the question but the given heat capacities of water from a previous question was 4180 J/kg °C and porcelain was 107.)

Relevant Equations

Q=mc▲t, Qreleased + Qabsorbed = 0, T=Tf-Ti

Givens for water: m: 0.250kg of water
T_W : 95°C
C=4180

Givens for mug: m=0.085kg
T_M : 19°
c=107

Required: final temperature of water

Analysis/Solution: Qreleased+Qabsorbed=0, q=mc▲t

m_w*c_w*T_w + m_p*c_p*T_p = 0

(0.250)(4180) (T₂-95) + (0.085)(107)(t₂-19)=0

1045(t₂-95) + 9.095(t₂-19)=0

1045T₂-99275 + 9.095T₂-172.805=0

1054.095T₂ - 99447.805 = 0

99447.805/1054.095 = t2

t2=94

Statement: The final temperature of the water for his tea was 94 degreesI'm not sure here if what I did with the temperature was correct, or if I made a mistake somewhere else. (I would also appreciate if you guys tell me if my formatting is acceptable/too hard too look at?)

 

[haruspex]

Problem Statement: Mr. Gryphon was taking a break between classes and decided to make himself a cup of tea. He poured 250g of water at 95°C into an 85g porcelain mug which had an initial temperature of 19°C. What was the final temperature of the water for his tea? ( Not technically part of the question but the given heat capacities of water from a previous question was 4180 J/kg °C and porcelain was 107.)
Relevant Equations: Q=mc▲t, Qreleased + Qabsorbed = 0, T=Tf-Ti

Givens for water: m: 0.250kg of water
T_W : 95°C
C=4180

Givens for mug: m=0.085kg
T_M : 19°
c=107

Required: final temperature of water

Analysis/Solution: Qreleased+Qabsorbed=0, q=mc▲t

m_w*c_w*T_w + m_p*c_p*T_p = 0

(0.250)(4180) (T₂-95) + (0.085)(107)(t₂-19)=0

1045(t₂-95) + 9.095(t₂-19)=0

1045T₂-99275 + 9.095T₂-172.805=0

1054.095T₂ - 99447.805 = 0

99447.805/1054.095 = t2

t2=94

Statement: The final temperature of the water for his tea was 94 degreesI'm not sure here if what I did with the temperature was correct, or if I made a mistake somewhere else. (I would also appreciate if you guys tell me if my formatting is acceptable/too hard too look at?)

All good.