The answer is: [D]: " 417 cm³ " .
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Step-by-step explanation: Use the formula:
V₁ /T₁= V₂ /T₂ ;
in which: V₁ = initial volume = 556 cm³ ;
T₁ = initial temperature = 278 K ;
V₂ = final ("new") temperature = 308 K
T₂ = final ("new:) volume = ?
Solve for "V₂" ;
Since: V₁ /T₁= V₂ /T₂ ;
We can rearrange this "equation/formula" to isolate "V₂" on one side of the equation; and then we can plug in our know values to solve for "V₂" ;
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V₁ /T₁= V₂ /T₂ ; Multiply EACH side of the equation by "T₂ " :
→ T₂ (V₁ /T₁) = T₂ (V₂ /T₂) ;
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to get:
↔ T₂ (V₂ /T₂) = T₂ (V₁ /T₁) ;
→ V₂ = T₂ (V₁ /T₁) ;
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Now, plug in our known values, to solve for "V₂" ;
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→ V₂ = T₂ (V₁ /T₁) ;
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→ V₂ = 308 K ( 556 cm³ /278 K) ;
→ The units of "K" cancel to "1" ; and we have:
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→ V₂ = 308*( 556 cm³ / 278 ) = [(208 * 556) / 278 ] cm³ ;
Note: We will keep the units of volume as: "cm³ "; since all the answer choices given are in units of: "cm³ " ; {that is, "cubic centimeters"}.
→ [(208 * 556) / 278 ] cm³ = [ (115,648) / (278) ] cm³ ;
→ For the "(115,648)" ; round to "3 (three significant figures)" ;
→ "(115,648)" → rounds to: "116,000" ;
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→ (116,000) / (278) = 417.2661870503597122 ;
→ round to 3 significant figures; → "417 cm³ " ;
→ which corresponds with "choice [D]".
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The answer is: [D]: "417 cm³ " .
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