(0.2kg)(4190J/kg.degree Celsius)(T-70 degrees Celsius)+(0.1kg)(390J/kg.degree Celsius)(T-20 degrees Celsius)= 0.
how will I equate it to get the final Temperature? I don't understand how did they get the answer of T=67.8 degrees Celsius.
can someone explain it? Pls. I have an Exam tomorrow and I need to understand it. thanks
Just do the algebra to get the final T. Stick the units (degrees C) on later.
838.2*(T-70)+ 39(T-20)=0
(838.2+39) T = 58764 + 5800
T = 64564/878.2 = 73 C
To solve the equation and find the value of temperature (T), we can follow these steps:
Step 1:
Expand the equation by multiplying each term by the respective coefficient:
(0.2kg)(4190J/kg°C)(T-70°C) + (0.1kg)(390J/kg°C)(T-20°C) = 0
Step 2:
Distribute the coefficients to each term within the parentheses:
(0.2kg)(4190J/kg°C)(T) - (0.2kg)(4190J/kg°C)(70°C) + (0.1kg)(390J/kg°C)(T) - (0.1kg)(390J/kg°C)(20°C) = 0
Step 3:
Combine like terms by rearranging and simplifying:
[(0.2kg)(4190J/kg°C)(T)] + [(0.1kg)(390J/kg°C)(T)] = [(0.2kg)(4190J/kg°C)(70°C)] + [(0.1kg)(390J/kg°C)(20°C)]
[(0.2)(4190)(T)] + [(0.1)(390)(T)] = [(0.2)(4190)(70)] + [(0.1)(390)(20)]
Step 4:
Simplify both sides of the equation:
836T + 39T = 58540 + 780
875T = 59320
Step 5:
Isolate the variable T by dividing both sides by 875:
T = 59320 / 875
Step 6:
Evaluate the resulting quotient to find the value of T:
T ≈ 67.88571
Step 7:
Round the value of T to the appropriate number of decimal places according to the given temperature values, which is 1 decimal place:
T ≈ 67.9 degrees Celsius
Therefore, the final temperature T is approximately equal to 67.9 degrees Celsius.