Question:medium

Initially a body is at a temperature of $50^{\circ}C$. If the temperature of the body is increased by $54^{\circ}F$, then its final temperature will be:

Show Hint

Remember the conversion: $T(^{\circ}F) = \frac{9}{5} T(^{\circ}C) + 32$.
Updated On: Jun 6, 2026
  • $80^{\circ}F$
  • $90^{\circ}C$
  • $176^{\circ}C$
  • $176^{\circ}F$
Show Solution

The Correct Option is D

Solution and Explanation

Step 1: Read the change carefully.
The body starts at $50^{\circ}\text{C}$ and its temperature is raised by $54^{\circ}\text{F}$. This is a rise of 54 Fahrenheit degrees, which is a change in temperature, not a final reading.
Step 2: Convert a change, not a reading.
A temperature change converts using the size of the degrees only: \[ \Delta T(^{\circ}\text{C}) = \frac{5}{9}\,\Delta T(^{\circ}\text{F}). \] The $+32$ in the usual formula is only for fixed readings, so we do not use it for a change.
Step 3: Find the rise in Celsius.
$\Delta T = \dfrac{5}{9}\times 54 = 30^{\circ}\text{C}$.
Step 4: Final temperature in Celsius.
Final $= 50 + 30 = 80^{\circ}\text{C}$.
Step 5: Match it to the options.
Change $80^{\circ}\text{C}$ to Fahrenheit: $F = \dfrac{9}{5}(80) + 32 = 144 + 32 = 176^{\circ}\text{F}$. So the final temperature $80^{\circ}\text{C}$ is the same as $176^{\circ}\text{F}$.
Step 6: Conclusion.
The final temperature is $176^{\circ}\text{F}$, which equals $80^{\circ}\text{C}$. \[ \boxed{176^{\circ}\text{F}} \]
Was this answer helpful?
0