A balloon with a volume of 5.3 L is taken from an indoor temperature of 24 C to the outdoors. The volume of the balloon outside is 4.9 L. How do you determine the C temperature outside?

Question

A balloon with a volume of 5.3 L is taken from an indoor temperature of 24 C to the outdoors.  The volume of the balloon outside is 4.9 L.  How do you determine the C temperature outside?

Jeremiah Adams · Accepted Answer

The outside temperature is 0 °C.

Given The volume #V_1# of a gas at a temperature #T_1#. A second volume #V_2# Find The second temperature #T_2# Strategy A problem involving two gas volumes and two temperatures must be a Charles' Law problem. The formula for Charles' Law is #color(blue)(|bar(ul(color(white)(a/a) V_1/T_1 = V_2/T_2color(white)(a/a)|)))" "# Solution We can rearrange Charles' Law to get #T_2 = T_1 × V_2/V_1# In your problem, #V_1 = "5.3 L"#; #T_1 = (24 + 273.15) K = "297.15 K"# #V_2 = "4.9 L"#; #T_2 = "?"# ∴ #T_2 = "297.15 K" × (4.9 cancel("L"))/(5.3 cancel("L")) = "274 K"# #"200 K" = "(274 - 273.15) °C" = "0 °C"# The outside temperature is 0 °C.

Axel Alvarado · Answer

undefined To determine the temperature outside, you can use the combined gas law, which states: (P1 * V1) / T1 = (P2 * V2) / T2. Rearrange the equation to solve for T2: T2 = (P2 * V2 * T1) / (P1 * V1). Substitute the given values: P1 (indoors) is atmospheric pressure at 24°C, V1 is the initial volume (5.3 L), P2 (outdoors) is atmospheric pressure, V2 is the final volume (4.9 L), and T1 is the initial temperature (24°C). Calculate T2 using the equation.